Locality, Complex Numbers, and Relativistic Quantum Theory

Abstract
A heuristic comparison is made of relativistic and non-relativistic quantum theory. To this end the Segal approach is described for the non-specialist. The significance of antimatter to the local and microcausal properties of the fields is laid bare. The fundamental difference between relativistic and non-relativistic (complex) fields is traced to the existence of two kinds of complex numbers in the relativistic case. Their relation to covariant and Newton-Wigner locality is formulated.
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    David Wallace (2009). QFT, Antimatter, and Symmetry. Studies in History and Philosophy of Science Part B 40 (3):209-222.
    Jonathan Bain (2011). Quantum Field Theories in Classical Spacetimes and Particles. Studies in History and Philosophy of Science Part B 42 (2):98-106.
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